Elements of GeometryW.J. Gage & Company, 1881 |
Dall'interno del libro
Risultati 1-5 di 23
Pagina 8
... shewn that BC is equal to BG , wherefore AL and BC are each of them equal to BG ; Ld things that are equal to the same thing are equal to one another ; therefore the straight line AL is equal to BC . ( ax . 1. ) Wherefore from the given ...
... shewn that BC is equal to BG , wherefore AL and BC are each of them equal to BG ; Ld things that are equal to the same thing are equal to one another ; therefore the straight line AL is equal to BC . ( ax . 1. ) Wherefore from the given ...
Pagina 9
... shewn to coincide with the point E ; wherefore the base BC shall coincide with the base EF ; because the point B coinciding with E , and C with F , if the base BC do not coincide with the base EF , the two straight lines BC and EF would ...
... shewn to coincide with the point E ; wherefore the base BC shall coincide with the base EF ; because the point B coinciding with E , and C with F , if the base BC do not coincide with the base EF , the two straight lines BC and EF would ...
Pagina 17
... shewn to be equal to two right angles ; wherefore the angles CEA , AED are equal to the angles AED , DEB ; take away from each the common angle AED , and the remaining angle CEA is equal to the remaining angle DEB . ( ax . 3. ) In the ...
... shewn to be equal to two right angles ; wherefore the angles CEA , AED are equal to the angles AED , DEB ; take away from each the common angle AED , and the remaining angle CEA is equal to the remaining angle DEB . ( ax . 3. ) In the ...
Pagina 19
... shewn to be not equal to AB ; therefore AC is greater than AB . Wherefore the greater angle , & c . Q.E.D. PROPOSITION XX . THEOREM . Any two sides of a triangle are together greater than the third side . Let ABC be a triangle . Then ...
... shewn to be not equal to AB ; therefore AC is greater than AB . Wherefore the greater angle , & c . Q.E.D. PROPOSITION XX . THEOREM . Any two sides of a triangle are together greater than the third side . Let ABC be a triangle . Then ...
Pagina 21
... shewn that BA , AC are greater than BE , EC ; much more then are BA , AC greater than BD , DC . Again , because the exterior angle of a triangle is greater than the interior and opposite angle ; ( I. 16. ) therefore the exterior angle ...
... shewn that BA , AC are greater than BE , EC ; much more then are BA , AC greater than BD , DC . Again , because the exterior angle of a triangle is greater than the interior and opposite angle ; ( I. 16. ) therefore the exterior angle ...
Parole e frasi comuni
AB is equal AC is equal adjacent angles algebraical alternate angles angle ABC angle ACB angle AGH angle BAC angle contained angle EDF angle equal axiom base BC bisected circle definition demonstration diagonals double equal angles equal to AC equal to twice equilateral triangle Euclid Euclid's Elements exterior angle Geometrical given line given point given straight line gnomon greater hypotenuse interior and opposite isosceles triangle join Let ABC line BC line be divided linear units lines be drawn magnitude meet opposite angles opposite sides parallel straight lines parallel to BC parallelogram perpendicular porism problem produced Prop proved Q. E. D. PROPOSITION quadrilateral rectangle AC rectangle contained remaining angle right angles right-angled triangle segments shew shewn side BC square described square on AC THEOREM trapezium triangle ABC twice the rectangle unequal vertex wherefore